HomeschoolMathonline.com is a powerful free resource for homeschooling students, parents and teachers. The site includes comprehensive math instruction (by John Zimmerman) that mostly focuses on middle and high school mathematics. The goal of the site is to get homeschool students to truly understand the core math concepts and skills that are essential for mastery of college prep math.

One of the most important skills for high school level math is the ability to factor. Much of the factoring Algebra 1 and 2 students focus on is factoring polynomials. However there are many other non-polynomial expressions that we factor as well in algebra so it’s not only about polynomials like trinomials. By the time your child finishes Algebra 2 they should be able to handle a factoring problem like the one below.I would classify this problem as moderately challenging/average

so I would expect most students at this level to be able to handle it. If you have a few minutes this problem would be a good little pop quiz for your homeschooler. I would give them up to 5 min to finish. Also I would let them use their notes or books.

Ok here’s the problem- simplify the following:

Here is the solution:

The essence of what I’m looking for in this problem is your child’s ability to recognize special factoring rules. The special rules that we use in this problem are “the difference of two squares” and the “difference of two cubes”. Now don’t let the word “special” throw you off by thinking we don’t use these rules frequently in algebra- we do!

By the time your child finishes Algebra 2 they should have learned these rules and understand how to apply the formulas. Of course the skill may not be fresh in your child’s memory so that’s why I allow 5 min and the use of their notes and books. Hopefully your child saw the pattern of the problem and they were able to do it pretty fast. However if your homeschooler did not get the problem correct just make a note to yourself that your child needs more practice factoring- the extra review and effort will serve them well in their mathematics future.